- #1

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I'm trying to simplify the combination defined as : [itex]\binom{n}{\frac{n}{2}}[/itex].

I did some calculations, starting from the factorial formula [itex]\frac{n!}{(\frac{n}{2})!(\frac{n}{2})!}[/itex] and i found this form :

[itex]2^{n}(1-\frac{1}{n})(1-\frac{1}{n-2})(1-\frac{1}{n-4})...[/itex]

but i don't know how to continue, can you help me ?

I did some calculations, starting from the factorial formula [itex]\frac{n!}{(\frac{n}{2})!(\frac{n}{2})!}[/itex] and i found this form :

[itex]2^{n}(1-\frac{1}{n})(1-\frac{1}{n-2})(1-\frac{1}{n-4})...[/itex]

but i don't know how to continue, can you help me ?